Problem 15E

At a certain fast-food restaurant, 25% of drink orders are for a small drink, 35% for a medium, and 40% for a large. A random sample of 20 orders is selected for audit.

a. What is the probability that the numbers of orders for small, medium and large drinks are 5, 7, and 8, respectively?

b. What is the probability that more than 10 orders are for large drinks?

Solution :

Step 1 of 2:

Let denotes the 3 drinks.

Where,

is the small drink it is 25%.

is the medium drink it is 35% and

is the large drink it is 40%.

The number of drinks among the 20 orders.

Here ,,=0.40.

So MN(20,0.25,0.35,0.40)

Our goal is :

a). We need to find the probability that the numbers of orders for small,medium and large drinks

are 5,7, and 8.

b). We need to find the probability that more than 10 orders are for large drinks.

a).

Now we have to find the probability that the numbers of orders for small,medium and large drinks are 5,7, and 8.

The multinomial probability formula is given by

P(,,=OR

P(,,)=

We consider 5,,and n=20.

Then the the probability that the numbers of orders for small,medium and large drinks are 5,7, and 8 is

P(=5,=7,=8)=

P(=5,=7,=8)=

P(=5,=7,=8)= 99768240

P(=5,=7,=8)= 0.0411.

Therefore the probability that the numbers of orders for small,medium and large drinks are 5,7, and 8 is 0.0411.